Question

Porównaj liczby.
a) 22³³ i 33²²
b)333⁴⁴⁴ i 444³³³
Proszę o dokładne rozwiązanie bez użycia kalkulatora :P
Będę usuwał takie odpowiedzi :D

Answer 1

A) 22³³ i 33²²
* - mnożenie

22³³ = (2 * 11)³³ = 2³³ * 11³³ = (2³)¹¹ * (11³)¹¹ = 8¹¹ * (11³)¹¹ =
(8 * 11³)¹¹
33²² = (3 * 11)²² = 3²² * 11²² = (3²)¹¹ * (11²)¹¹ = 9¹¹ * (11²)¹¹ =
(9 * 11²)¹¹

(8 * 11³)¹¹ > (9 * 11²)¹¹

b) 333⁴⁴⁴ i 444³³³
333⁴⁴⁴ = (3 * 111)⁴⁴⁴ = 3⁴⁴⁴ * 111⁴⁴⁴ = (3⁴)¹¹¹ * (111⁴)¹¹¹ =
(3⁴ * 111⁴)¹¹¹ = (81 * 111⁴)¹¹¹
444³³³ = (4 * 111)³³³ = 4³³³ * 111³³³ = (4³)¹¹¹ * (111³)¹¹¹=
(4³ * 111³)¹¹¹ = (64 * 111³)¹¹¹

(81 * 111⁴)¹¹¹ > (64 * 111³)¹¹¹